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C₂×#18082 #6345125

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(3,4,9,13)(5,14,6,11)(7,12,8,17)(10,16,18,15)(19,20,24,27,23,26,32,34)(21,28,30,31,29,25,33,22);(3,5,9,6)(4,10,13,18)(7,15,8,16)(11,17,14,12)(19,21)(20,25)(22,27)(23,29)(24,30)(26,28)(31,34)(32,33);(3,6,9,5)(4,11,13,14)(7,15,8,16)(10,17,18,12)(19,22,24,28,23,31,32,25)(20,21,27,30,26,29,34,33);(3,7,9,8)(4,12,13,17)(5,15,6,16)(10,11,18,14)(21,29)(22,31)(25,28)(30,33)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252321);